Discontinuous Galerkin Finite Elements for the Einstein Equations

Abstract: Discontinuous Galerkin Finite Element (DGFE) methods offer a mathematically beautiful, computationally efficient, and efficiently parallelizable way to solve hyperbolic partial differential equations. These properties make them highly desirable for numerical calculations in relativistic astrophysics. I will introduce DGFE as discretization method and describe our approach to applying them to the Einstein equations in the BSSN formulation. I will also illustrate what constitutes an efficient algorithm on current computing hardware, and why DGFE methods are thus today a priori a much better choice than many other higher-order discretization methods.